1. **State the problem:** Investigate the relationship between net force, mass, and acceleration using the experimental setup with a trolley, pulley, and hanging masses. 2. **Variables:** - Independent variable: Mass of hanging pieces (kg) - Dependent variable: Acceleration (m/s²) - Constant variable: Mass of the trolley 3. **Investigative question:** How does the net force applied to the trolley affect its acceleration? 4. **Purpose of hanging mass:** The hanging mass creates a net force due to gravity ($F_{net} = mg$) that causes the trolley to accelerate, demonstrating the relationship between force, mass, and acceleration. 5. **Formula used:** Newton's second law: $$F_{net} = ma$$ where $F_{net}$ is net force, $m$ is total mass, and $a$ is acceleration. 6. **Calculations for acceleration:** - Acceleration is the gradient of the velocity vs time graph: $$a = \frac{\Delta v}{\Delta t}$$ - Calculate $F_{net} = mg$ for each hanging mass. - Use the total mass (trolley + hanging mass) for $m$. - Calculate acceleration $a$ from the velocity-time graph. 7. **Example calculation:** - Suppose hanging mass $m_h = 0.03$ kg (3 x 10 g), $g = 9.8$ m/s² - $$F_{net} = m_h g = 0.03 \times 9.8 = 0.294\,N$$ - If total mass $m = m_{trolley} + m_h$, and velocity changes from 0 to 1.5 m/s in 2 s, - $$a = \frac{1.5 - 0}{2 - 0} = 0.75\,m/s^2$$ 8. **Graph:** Plot acceleration ($a$) on the y-axis vs net force ($F_{net}$) on the x-axis. The graph should be linear. 9. **Gradient of graph:** The gradient equals $$\frac{\Delta a}{\Delta F_{net}} = \frac{1}{m}$$ which represents the inverse of the total mass. 10. **Conclusion:** Acceleration is directly proportional to net force and inversely proportional to mass, confirming Newton's second law: $$a = \frac{F_{net}}{m}$$. **Slug:** force acceleration **Subject:** physics **desmos:** {"latex":"y=x/m","features":{"intercepts":true,"extrema":true}} **q_count:** 3